Least Common Multiple (LCM) of 122 and 196
The least common multiple (LCM) of 122 and 196 is 11956.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 122 and 196?
First, calculate the GCD of 122 and 196 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 122 ÷ 196 = 0 remainder 122 |
| 2 | 196 ÷ 122 = 1 remainder 74 |
| 3 | 122 ÷ 74 = 1 remainder 48 |
| 4 | 74 ÷ 48 = 1 remainder 26 |
| 5 | 48 ÷ 26 = 1 remainder 22 |
| 6 | 26 ÷ 22 = 1 remainder 4 |
| 7 | 22 ÷ 4 = 5 remainder 2 |
| 8 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 135 and 80 | 2160 |
| 120 and 130 | 1560 |
| 143 and 200 | 28600 |
| 122 and 13 | 1586 |
| 16 and 50 | 400 |